During the summer months, the water level in Marta’s pool decreases by about (1)/(2) inch each day due to evaporation. Which equation shows the approximate total change, in inches, to the water level in her pool after 30 summer days?
The Correct Answer and Explanation is:
Correct Answer:
$$
\text{Total Change} = \frac{1}{2} \times 30
$$
Explanation (300+ words):
To determine the total change in water level in Marta’s pool over 30 summer days, we need to understand how much water is lost each day and then multiply that by the number of days.
According to the question, the water level in the pool decreases by about $\frac{1}{2}$ inch per day due to evaporation. The term “decrease” means that the water level is going down each day.
If we want to find the total change over a period of 30 days, we multiply the amount of daily decrease by the number of days:
$$
\text{Total Change} = \text{Daily Decrease} \times \text{Number of Days}
$$
$$
\text{Total Change} = \frac{1}{2} \times 30
$$
Now let’s calculate this:
$$
\frac{1}{2} \times 30 = \frac{30}{2} = 15
$$
So, the total decrease in the water level after 30 days is 15 inches.
However, since the question is asking for the equation that represents the change, the correct response is not just the number 15, but the expression that leads to that number. That expression is:
$$
\frac{1}{2} \times 30
$$
This expression accurately models the situation described: a daily decrease of $\frac{1}{2}$ inch over a 30-day period.
Summary:
- Daily decrease: $\frac{1}{2}$ inch
- Time period: 30 days
- Total decrease: $\frac{1}{2} \times 30 = 15$ inches
The equation that represents this situation is:
$$
\boxed{\frac{1}{2} \times 30}
$$